In my opinion, for poly to work, there has to be a strict "no lies" policy. This includes lies by omission. You work out very explicitly the things that are important to you both - this may be where you are, who you are with, whether or not you are having sex, etc. Different relationships require different levels of disclosure, depending on the needs of the individuals involved. Some willingly allow the partner to read emails and texts, others don't. There is no cookie-cutter way of laying this out.
So lying about anything, or omitting to talk about something that you have both agreed is important to disclose is breaking the rules of your relationship and thus, cheating.
You folks are new to poly, so this sort of thing is quite likely to happen - but it sounds like you are learning from it. We all have patterns of behaviour pre-programmed into us, and it can take some work to reprogram them - but it really has to be done in order to make this work.
"Listen, or your tongue will make you deaf." - Native American Proverb